Finite Group Databasebeta

← C2×#19152435 #26035061

Subgroups — C2×#19152435 #26035061

Order 11392.

5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.

normal subgroups only

This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19152435C2132yesmaximal, direct product factor
2C2×#15668060C215yesmaximal, complemented
3C2×#15668058C2110yesmaximal, complemented
4C22×#13083575C215yesmaximal, complemented
5C2×#41×D89C2110yesmaximal, complemented
6C2×2−1+4×C89C211yesmaximal, characteristic, complemented
7#15668060C22180yescomplemented
8#15668058C221160yescomplemented
9C2×#13083575C22110yescomplemented
10C2×#13083575C22120yescomplemented
11C2×#13083575C22180yescomplemented
12C2×#13083574C22130yescomplemented
13C2×#13083573C22110yescomplemented
14#41×D89C221160yescomplemented
15C2×Q8×D89C22110yescomplemented
16C22×D356C22115yescomplemented
17C2×D4×D89C22130yescomplemented
18C22×C4×D89C22115yescomplemented
192−1+4×C89C22116yescomplemented
20C2×#41×C89C22110yescomplemented
21C22×Q8×C89C2215yescomplemented
22C23×D89C23115yes—
23#13083575C23180yescomplemented
24#13083575C231160yescomplemented
25#13083574C231240yescomplemented
26#13083573C23180yescomplemented
27C2×Dic178C23110yes—
28Q8×D89C23180yescomplemented
29C2×D356C23130yes—
30C2×D356C231120yescomplemented
31C2×C22⋊D89C23120yes—
32D4×D89C231240yescomplemented
33C22×Dic89C2315yes—
34C2×C4×D89C23110yes—
35C2×C4×D89C23130yes—
36C2×C4×D89C231120yescomplemented
37#41×C89C23180yescomplemented
38C2×Q8×C89C23110yes—
39C2×Q8×C89C23140yescomplemented
40C2×D4×C89C23110yes—
41C22×C4×C89C23115yes—
42C23×C89C2415yes—
43C22×D89—430no—
44C22×D89C24110yes—
45C22×D89C24160yes—
46Q8×C89C24140yes—
47D4×C89C24140yes—
48C2×C4×C89C24110yes—
49C2×C4×C89C24160yes—
50C22⋊D89C24180yes—
51C2×Dic89C2411yescharacteristic
52C2×Dic89C2415yes—
53C2×Dic89C24120yes—
54D356C241120yes—
55C4×D89C24140yes—
56C4×D89C241120yes—
57Dic178C24140yes—
58C22×C89—210no—
59C22×C89C25110yes—
60C22×C89C2511yescharacteristic
61C2×D89—220no—
62C2×D89—460no—
63C2×D89C25120yes—
64C4×C89C25120yes—
65Dic89C25110yes—
66Dic89C2512yes—
67C2×C89—210no—
68C2×C89#58512yescomplemented
69C2×C89C2611yescharacteristic
70D89—220no—
71C2×#585—891nomaximal, Sylow
72C89C2×#58511yescharacteristic, complemented, Sylow
73#585—8932no—
74C2×2−1+4—895no—
75C2×2−1+4D8911yescharacteristic, complemented
76C2×H(5,𝔽2)—8910no—
77C22×#41—8910no—
78C22×#41—895no—
792−1+4—8980no—
802−1+4C2×D89116yescomplemented
81H(5,𝔽2)—89160no—
82C2×#41—89160no—
83C2×#41—8910no—
84C2×#41—8920no—
85C2×#41—8980no—
86C2×#41—8910no—
87C2×#41—8930no—
88C2×#41C2×D89110yescomplemented
89C22×Q8—8910no—
90C22×Q8C2×D8915yescomplemented
91C22×D4—8930no—
92C22×D4—8915no—
93C23×C4—8915no—
94C24—8915no—
95#41—8980no—
96#41—89160no—
97#41—8980no—
98#41—89240no—
99#41C22×D89180yescomplemented
100C2×Q8—8980no—
101C2×Q8—8910no—
102C2×Q8C22×D89110yes—
103C2×Q8C22×D89140yescomplemented
104C2×D4—8920no—
105C2×D4—89240no—
106C2×D4—8930no—
107C2×D4—89120no—
108C2×D4C22×D89110yes—
109C22×C4—895no—
110C22×C4—8910no—
111C22×C4—8930no—
112C22×C4—89120no—
113C22×C4C22×D89115yes—
114C23—8960no—
115C23—8910no—
116C23—35630no—
117C23C23×D8915yes—
118Q8—8940no—
119Q8C23×D89140yes—
120D4—8980no—
121D4—89120no—
122D4C23×D89140yes—
123C2×C4—8920no—
124C2×C4—891no—
125C2×C4—895no—
126C2×C4—8940no—
127C2×C4—89120no—
128C2×C4C23×D89160yes—
129C2×C4C23×D89110yes—
130C22—210no—
131C22—8920no—
132C22—35660no—
133C22—17820no—
134C22C24×D89110yes—
135C22C24×D8911yescharacteristic
136C4—892no—
137C4—8910no—
138C4C24×D89120yes—
139C2—210no—
140C2—17820no—
141C2#1915243512yesdirect product factor
142C2C25×D8911yescharacteristic
subgroupG/H
centerC22C24×D89
commutator, cosocleC2×C89C26
FrattiniC2C25×D89
FittingC2×2−1+4×C89C2
socleC22×C89C25
hypercenterC2×2−1+4D89
hypocenterC89C2×#585
LCSG ▷ C2×C89 ▷ C89
UCSC1 ◁ C22 ◁ C2×2−1+4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #19152435C2direct (N × H)
2. C2×#15668060C2semidirect
3. C2×#15668058C2semidirect
4. C22×#13083575C2semidirect
5. C2×#41×D89C2semidirect
6. C2×2−1+4×C89C2semidirect
7. #15668060C22semidirect
8. #15668058C22semidirect
9. C2×#13083575C22semidirect
10. C2×#13083575C22semidirect
11. C2×#13083575C22semidirect
12. C2×#13083574C22semidirect
13. C2×#13083573C22semidirect
14. #41×D89C22semidirect
15. C2×Q8×D89C22semidirect
16. C22×D356C22semidirect
17. C2×D4×D89C22semidirect
18. C22×C4×D89C22semidirect
19. 2−1+4×C89C22semidirect
20. C2×#41×C89C22semidirect
21. C22×Q8×C89C22semidirect
23. #13083575C23semidirect
24. #13083575C23semidirect
25. #13083574C23semidirect
26. #13083573C23semidirect
28. Q8×D89C23semidirect
30. C2×D356C23semidirect
32. D4×D89C23semidirect
36. C2×C4×D89C23semidirect
37. #41×C89C23semidirect
39. C2×Q8×C89C23semidirect
68. C2×C89#585semidirect
72. C89C2×#585semidirect
75. C2×2−1+4D89semidirect
80. 2−1+4C2×D89semidirect
88. C2×#41C2×D89semidirect
90. C22×Q8C2×D89semidirect
99. #41C22×D89semidirect
103. C2×Q8C22×D89semidirect
141. C2#19152435direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191524352
C2×#156680602
C2×#156680582
C22×#130835752
C2×#41×D892
C2×2−1+4×C892
C2×#58589